Another drawback of Theorem REF  is a possible deterioration of the statements for large dimensions. In many cases, we have a family of Lie groups, such as the family of unitary groups \(\lbrace U(d)\rbrace _{d=1}^\infty \) , whose dimension grows to infinity. In this case, the size of the stability basin of Theorem REF  compared to the whole group diminishes exponentially as the dimension parameter grows to infinity. Thus, in practice, it would be desirable to obtain dimension-independent bounds for Theorem REF . This is possible for the Lohe model REF , by using the operator norm instead of the Frobenius norm, as can be checked by modifying the arguments of [1]} in a straightforward manner.
